“Thanks for all the well wishes about our new baby boy,” Dallas, 32, Tweeted Tuesday. “We are in LOVE! He’s our favorite person.”

“Both mom and baby are doing great,” their rep tells PEOPLE.
The couple have not yet released the name of their son, although Goodwin, 36, has said they’ve put a lot of thought into choosing it.

“Naming a child with the last name of ‘Dallas,’ is a little more complicated,” she said last month — but the couple have definitely been doing their research.

“We read so many books. I can’t even tell you. I could probably teach a college-level course in bringing up a child,” Dallas joked recently. “It doesn’t mean I’ll be great at it, but I hope I’m good at it.”

Congrats to the new Mommy and Daddy! May the road rise up to meet you all!

Anonymous
on May 31st, 2014

Congrats to them! Can’t wait to hear the name!

klutzy_girl
on May 31st, 2014

Congratulations! Really can’t wait to hear the baby’s name.

SAR
on May 31st, 2014

That’s great! On the show their baby was a boy, so it’s cool that their real life baby is a boy too. They’re a cute couple.

Tay
on May 31st, 2014

Congrats to Josh and Ginnifer!

Guest
on June 1st, 2014

Happy for them on screen and off.

Hea
on June 3rd, 2014

Yay, finally! Congratulations!

Pam
on June 3rd, 2014

@SAR on the show their baby is a girl, Emma-the main character. She had a son.

deaf1dog
on June 3rd, 2014

@Pam. In the next to the last episode of OUAT, Snow gave birth to a baby boy who they named Neal. The Wicked Witch then kidnapped him to help with her time travel plan. Everybody banded together and they rescued him.

Milly
on June 3rd, 2014

@Pam I think SAR is talking about the son Snow gave birth to few episodes before the end of the last season, Emma’s new baby brother :-)

Trish
on June 3rd, 2014

@Pam….you must have missed the entire last season!!! Snow and Charming had ANOTHER child and it was a boy. They revealed his last name as Neil on the very final episode. Emma is their daughter and yes she has a son named Henry, but they now have a son too.

Eliz
on June 3rd, 2014

They’d better figure out pretty quickly that they’re each others’ favorite person or the marriage is not going to go the distance. Children are ours for a short time but the spouse should be forever. Too many couples turn away from the spouse and have the child takeover that spot and when the kids are gone, can’t figure out what happened to the marriage. Your spouse and the marriage have to come first.

well, his last name doesn’t have to be Dallas. It can be anything you want. My only child doesn’t have the same surname as either of his parents.

Marie
on June 4th, 2014

Why not Charming Dallas? ahahah :)

Alissa
on June 4th, 2014

Cute name. Ginnifer seems like a person who would love the name Oliver….cute and a bit old-fashioned…the name and Ginnifer. I just love her…she always seems so sweet and sincere.

Chloe
on June 4th, 2014

LOVE that name, its my favorite name for a little boy… congrats to the new family, can’t wait to see a picture of the baby, I bet he’s absolutely beautiful.

Amber
on June 4th, 2014

Didn’t she say she was choosing carefully with the last name of Dallas? Oliver = “all over” Dallas.

Anna
on June 4th, 2014

Cute name!

emma
on June 4th, 2014

Beautiful!! I love the name…congratulations again to the happy couple.

Lacey
on June 4th, 2014

Oliver Dallas is really hard to say. Love the name, it just doesn’t work with Dallas.

Jami
on June 4th, 2014

That’s a great strong Irish name I believe. Very Cute!!! Congrats to the Happy Couple and Prince Oliver Finlay Dallas!!! :)

Hilda
on June 4th, 2014

Cute couple, but is her name pronounced like “Ginn-infer”? If so, very odd.

robin
on June 4th, 2014

Oliver is such a cute name!!

Eli
on June 4th, 2014

Cheaters. How precious.

Nicole
on June 4th, 2014

I like the name they picked out. It’s very cute :)

Ivy.
on June 5th, 2014

@Hilda She was born “Jennifer” but since she’s Southern she didn’t like it when they called her JEN-infer so she changed it to GIN-nifer to make sure people pronounce it like a Southerner would.

I really enjoy the name, though I must admit it’s a bid saddening that TMZ announced his name without their consent. Ginnifer and Josh obviously didn’t announce it with his birth for a reason.

Brooklyn
on June 5th, 2014

Oliver Dallas sounds great. Great name. Not sure about Finlay but their choice!

micky
on June 5th, 2014

That’s beautiful name and its normal thank God.. Congratulations on your little bundle of joy Oliver

Anonymous
on June 5th, 2014

Ivy- I’m with you. They’ve done that to several other celebs as well (the most recent example being Kendra Wilkinson) and they really need to stop. Newsflash, TMZ, birth certificates being public record does NOT give you the right to announce their children’s names without their consent!

Jeanne
on June 5th, 2014

Congrats to them. However, I hate to point this out but Ginnifer said that she didn’t want her baby to have a destination name, like Austin Dallas. But Oliver Dallas kinda sounds like “all over Dallas.”

Lala
on June 5th, 2014

Pretty sleazy of TMZ, to announce their child’s name. If they wanted it blasted out to the media, they’d have done it themselves.

They haven’t released the name but TMZ thought it was okay to just check for it? And People jumped on the TMZ bandwagon. And I’m sure you have cameras at the ready to get that elusive “first pic”. Then there will be the “body after baby” layout.

KWW
on June 5th, 2014

So sweet! Hope they stay together!

West
on June 5th, 2014

What a nice name . Congratulations .

Guest
on June 5th, 2014

Lovely name, congrats!

EllaHella
on June 5th, 2014

I love the name. They’re a great couple.

Kimberly
on June 5th, 2014

Awww I’m sure Oliver is a cutie!! I love the name too, not something you hear everyday and also not something weird like the rest of Hollywood…congrats!! :) I really like Ginnifer, she is a great actress and I’m sure she will be a wonderful mommy!

Catherine
on June 5th, 2014

Pretty tacky thing to announce the name before the parents. Considering Ginnifer is Jewish, it’s tradition to wait for 8 days before announcing it at a Brit Milah. So sure, you get the scoop but you just stomped all over someone’s religious beliefs. Nicely done.

KL
on June 5th, 2014

Thats a cute name!! love it! Thanks for picking a normal name

Magnolia
on June 6th, 2014

@Catherine – When I found out she was Jewish, I was wondering the same thing. Many cultures have rituals and ceremonies for naming a baby. This was very rude.

lili
on June 6th, 2014

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Anonymous
on June 6th, 2014

Love their show ” Once Upon a Time”. Great actor and actress.

don444
on June 10th, 2014

Sorry, she still looks like a teenage boy who’s weirdly fond of donning his sister’s clothes.